I#m professional frontend web developer. Here's what i say.
"I am planning on making my front page with Construct 2. Only having my front page will help with the not indexed issue."
Intros are frustrating for users.
"How can I make a message appear if the html5 doesn't load suggesting upgrading the browser. And/or redirecting to the standard homepage?"
You can, using Java Script or php code, but not based on weather html5 loaded or not but based on the knowledge if the particular browser supports it or not, and make a conditions. Look in google for open source scripts. Not all are compatible with WP.
"Can I make an image in the construct iframe link to a page without opening a new browser (so in the same window)?"
Don't know.
"Couldn't you embed invisible text suggestions on the page which would make google take notice of it?"
Google will give you penalty for it.
"Where should I be looking to find out the best way to implement something like this into my website?"
Like what?
"Here is my website at the moment, definitely needs the POW which construct could give it!"
Your website needs good design and not construct!
All Best
Mik